Many industries and applications, such as water purification, chemical synthesis, pharmaceutical purification, refining, natural gas separation, and many other applications rely on energy-intensive membrane separation as a major component of their processes. The need for membranes with high selectivity and flux for both liquid-phase and gas-phase membranes has led to many improvements in ceramic and polymer-based membranes over the past few decades. One of the primary challenges has been maximizing flux while maintaining high selectivity. Typically, increasing flux rate necessitates a decrease in selectivity. While several decades of research has resulted in development of polymeric or ceramic membranes, further advances in membrane technology will likely rely on new membrane materials that provide better transport properties. Recent advances in two-dimensional (2D) materials such as graphene have opened new opportunities to advance membrane technology, where these 2D materials can form the active layer that confers selectivity.